1. Field of the Invention
This invention relates to a three dimensional crack and fracture morphology and propagation method for single and stacked directed surfaces that naturally incorporates external information.
2. Description of the Prior Art
A physical phenomenon, such as a fracture, fundamentally occurs in a discontinuous fashion. However, most methods for solving structural mechanics problems (e.g. the finite element method) are formulated to solve for continuous field variables. To model a crack in a continuum model requires embedding some model of discontinuity into the continuous formulation. Numerous approaches using this methodology have been introduced, such as X-FEM, cohesive cracks, element erosion, etc. These methods have achieved some degree of success. Purely discrete models, such as molecular dynamics (MD), can naturally evolve to open up discontinuities in a material. However, the number of molecules required for MD simulations capable of modeling practical engineering fracture problems is prohibitively large. Thus, there seems to be a place for a simple method to solve the continuum equations, but easily incorporate discontinuities.
The standard method of modeling composites is the continuum approach where the effect of the composite fibers is idealized as material properties of a linear elastic model. This is a form of the multiscale problem. The fibers themselves are too small a scale to be modeled explicitly and therefore this information is included in the model in the form of material properties. Even if the small scale of the fibers could be represented, the actual location in the matrix is knowledge that is difficult (if not impossible) to obtain with any reliable amount of certainty. The linear-elastic continuum approach works well for applications provided that the composite material properties are accurately determined. However, when failure is to be modeled, especially cracking, the information lost in the idealization of the fibers becomes critical. Cracking models based on continua will not predict the correct crack morphology due to the absence of actual fibers.
Moreover, for laminated composites, the fiber orientation has a profound effect on how cracks can propagate. In mesh-based analysis methods, the mesh orientation may influence the crack direction, but it may conflict with the physical requirements dictated by the fiber orientation.
Accordingly, what is needed is a method that explicitly models cracks and changing topology and is formulated to reduce or eliminate discretization choices from influencing the solution.
What is also needed is a method that naturally provides a mechanism for incorporating information that is not contained in the governing continuum equations to determine crack initiation and direction.
What is further needed is a method that returns physical knowledge to the model without the need to explicitly model fibers in the composite and enables the straightforward use of continuum mechanics to solve crack propagation problems in laminate fibrous composites which will model the physical behavior.
However, in view of the prior art considered as a whole at the time the present invention was made, it was not obvious to those of ordinary skill in the art how the limitations of the art could be overcome.